General ultracold scattering formalism with isotropic spin orbit coupling

TL;DR

This paper develops an analytical formalism for ultracold two-body scattering with isotropic spin-orbit coupling, revealing unique threshold behaviors and bound states, advancing understanding of SOC effects in ultracold quantum systems.

Contribution

It introduces a systematic method to solve coupled multichannel scattering problems with SOC and derives the exact Green's matrix for such systems.

Findings

Low energy threshold behavior modified by SOC

Existence of bound states for any negative scattering length

Confirmation of parity-breaking and handedness emergence

Abstract

A general treatment of ultracold two-body scattering in the presence of isotropic spin-orbit coupling (SOC) is presented. Owing to the mixing of different partial wave channels, scattering with SOC is in general a coupled multichannel problem. A systematic method is introduced to analytically solve a class of coupled differential equations by recasting the coupled channel problem as a simple eigenvalue problem. The exact Green's matrix in the presence of SOC is found, which readily gives the scattering solutions for any two identical particles in any total angular momentum subspace having negligible center of mass momentum. Application of this formalism to two spin-1 bosons shows the ubiquitous low energy threshold behavior for systems with isotropic SOC. A modified threshold behavior shows up, which does not occur for the spin-orbit coupled spin-1/2 system. We also confirm the parity-breaking mechanism for the spontaneous emergency of handedness, that has been proposed by Duan et. al. [1]. Additionally, a two-body bound state is found for any arbitrarily small and negative scattering length. Our study sheds light on the few-body side of SOC physics and provides one step towards understanding ultracold scattering in a non-Abelian gauge field.